13:23 Fux Gradus ad Parnassum pg 158 measure 3 and 8 seems to have a suspension of a kind you did not discuss (3-2 to 5-3?). Can you elaborate on why / how it works?
Good spot. I would probably figure these chords 9/3, depending on context. We could also call it a 3/2, but the figure "2" is often used when the bass tone is a dissonance (as with a 5/2 chord, for instance), which is not the case here. Bellermann ends up using this chord a couple of times in the exercise shown at the end of the video. These chords are similar to a 9-8 melodic suspension, but Fux's second species bass line allows the bass to change at the moment of resolution. If the bass had not changed, the suspension would resolve to an incomplete triad on the upbeat, which is also ok in free composition, but for a strict exercise we would prefer a complete triad in every measure. This also conveniently gets around the issue of anticipating the tone of resolution, since the bass has moved on by the time the resolution takes place.
What would be the correct doubling for a chord with a suspended 7th? For example, C major, the bass note is E and the figured bass is 7-6. Could the other voices, apart from the suspended one, be on Gs? This is a double 3rd for the 7th chord but when it resolves to 6 it is a doubled 5th for the tonic chord in first inversion which is more acceptable. 3:33 to make things clear, the dominant 7th is the only chord that can be freely struck; you don’t need to justify the dissonance? Any other 7th chord to replace both examples would be voice leading errors?
In a four voice texture, the figured bass symbol "7" in a context where it is clearly a 7-6 suspension implies an entire seventh chord, therefore there is also a chordal 5th (B in this case) that would move by step to double the 6th (C) in the chord of resolution or leap to another chord tone. If you wanted to avoid the fifth for whatever reason, then doubling the bass note (E) seems to be the most idiomatic. I have another video on the topic of what Kirnberger called the "essential" dissonance of the dominant seventh chord (video 11 in this playlist). Thoroughbass authors give the privilege of freely struck (unprepared) dissonances to this class of seventh chord, which is almost entirely the dominant seventh quality, but sometimes also includes fully diminished seventh chords or the half-diminished leading tone seventh chord, for instance in the case of Albrechtsberger's exercises in "free composition" from video 13 in the playlist. Of course, we are drifting quite a bit now from the strict counterpoint of Fux.
Hi Jacob- Just working through these again as it has been a while. In the 94-83 example. In bar 4 we have a dissonant 7thh above A. This 7th is not prepared, and yet is used as the preparation of another dissonance (4th). Why is this ok? Similarly, in bar 3, we have a dissonance between G sharp and D (dim 5th) moving to another dissonant 4th between A and D. It is my understanding that suspensions should be consonant tones carried over to form dissonances, thhis doesnt seem to be the case here! please explain?? thanks again!
Great question, as usual. More liberties are given in thoroughbass (free composition) than in counterpoint (strict composition), and many of these videos of mine show them juxtaposed next to one another as if they are part of the same tradition, which is potentially a source of confusion. The D in m. 3 is easier to explain so I'll start there. There are two possible explanations: 1) D is the chordal seventh of an E dominant seventh chord, and it is therefore an "essential" ("Wesentliche") dissonance and has a privilege in 18th-c theory to be introduced freely and to act as a preparation of a suspension (see video 11 in the playlist); 2) The note D could also be seen to have been prepared as a consonant tenth in m. 2, and so acted as a dissonance in both mm. 3 and 4 before resolving down by step in m. 4. Sechter's suspended G in m. 5 would not be appropriate in strict counterpoint. The preparation is a dissonant seventh, as you point out, and it also occurs on the last quarter note of the measure. However, Sechter allowed the chordal seventh (even of a minor quality seventh chord) to act as a preparation of a suspension in his thoroughbass examples when it followed a "circle of fifths" pattern like the sevenths that occurred on the weak beats in the example shown back around the 7:20 mark. The fact that it is prepared on the last quarter note probably has to do with the G-sharp of the previous measure; conceptually, the chordal seventh of an A minor chord could have been prepared as the third of an E chord moving through the circle of fifths like the pattern just mentioned, and could have been carried over mm. 3-5 just like the D in mm. 2-4, but we can't use both G-sharp and G-natural at the same time.
@@JacobGran Hi jacob, Yes, I see the logic here. I understand that Sechter allowed the chordal 7th to act as a preparation for a suspension, but would this 7th usually have been prepared in the previous chord? (unlike the 7th G here). So can this unprepared 7th G be seen as an outlier, introduced like this to avoid a cross relation? Or, would this 7th G be seen as an essential dissonance , introduced freely and able to act as a preparation for a suspension, even though it is not the 7th of a dominant chord?
Hi Jacob. Firstly, thanks for another great vid. I was working on the first given exercise here but I'm stumped on the penultimate chord (7-, 4-3). Both the 7th and the 4th are dissonant above the bass, but I cant prepare them properly as neither feature in the previous chord (Em). What to do here? thanks!
Good question. Let’s back up to the third to last measure; in the 9/7/4 chord there only the 9th and 7th resolve as the dash indicates that the fourth continues. That means we’re dealing with a cadential 6/4 triad for that measure (notes of a C major triad, not E minor), which is where the preparation for the fourth of the next measure comes from. The 7th in the penultimate measure is approached by step from the 8ve in the previous measure over a stationary bass, so it is actually a passing seventh (accented in this case) rather than a suspension and it too persists as the fourth resolves on the weak beat. I hope that helps.
@@JacobGran thanks very much for the explanation. i have a question regarding the second exercise. measure 4, we have a 652 chord. Is the harmony for this bar G7 in third inversion? What are the suspended notes here? The C is a non-chord note , prepared in the previous chord but is consonant with the bass. The G is a chord note (I think), but is not consonant with the bass, and doesn't seem to resolve by step in the next chord. I have only really come across melodic suspensions thus far, so am still getting to grips with suspension chords! thanks again! Ed
@@edbowles5497 Yes, that is right. The chord for that measure is a 6/4/2 chord built on F (an inversion of a G dominant seventh), with the chordal third, B, suspended by the note C. You are right to point out that this C is more consonant with the bass note, F, than the tritone to which it resolves, but that is just a consequence of how rich tonal harmony can be. I mentioned something similar in the example starting at 2:35. In my opinion the C sounds more like a 2-3 suspension (or 7-6, depending on how it is realized) with respect to the chord tone D than a suspension relative to the bass. As for the G not resolving, whenever the dissonance is shown as a "2" in the chord figures (like in 6/4/2 or 5/2, etc.) then the bass note is considered the dissonant note that must resolve, as the F does here (although not as a strict suspension, but as the "essential" dissonance of a dominant seventh chord; see the video on the counterpoint of dominant seventh chords for more on that). When the composer or analyst wants to indicate that the upper tone is the dissonance, it is typically figured as a "9" (as in 9/5/4 or something similar) instead of "2."
@@JacobGran Thanks yet again Jacob. I understand what youre saying, although I'm a bit lost when you talk about hearing the C as a suspension relative to D rather than the bass. I thought that harmony was the primary factor in defining what is being suspended and what isn't, and that suspensions by their very nature must happen relative to the bass? If the C was a 7-6 or 2-1 (you said 2-3 in your answer, but i take it you mean 2-1??) relative to D, then wouldn't that imply that D was the third of the chord? thanks for your help!
I could think of at least a few other chordal suspension combinations that aren't mentioned here, for example: 9/6 -> 8/5, 9/6/4 -> 8/5/3, 9/7/4 -> 8/6/3. Is this because they aren't very commonly used, or is there any other reason? Btw, I find the idea of resolving suspensions above a moving bass line very interesting. Coming from a jazz background, I just view them as chord change up until now :)
The suspension chords I looked at it this video are definitely not an exhaustive list, but they are the main chord types that I found discussed in thoroughbass and counterpoint manuals. I suspect that 9/6 -> 8/5 is not mentioned because the top voices moving in parallel fourths and finishing on perfect consonances is not idiomatic of suspensions. Suspensions that resolve to imperfect consonances are preferred, like 9/4 -> 8/3. I think a 9/6/4 chord would have to be prepared as 8/5/3 in the previous chord and then resolve to 8/5/3, which would mean that we are suspending parallel chords a step apart, which will sound like parallel octaves and fifths. Maybe the bass could move beneath the resolution, but its hard to picture. 9/7/4 is definitely possible, especially if it is prepared as the upper chord members of a dominant seventh chord.
Actually it just occurred to me that the 9/6/4 could be prepared as 10/7/5 of a dominant seventh chord, which would sound great over a deceptive cadence.
Hi Jacob. I am starting to get to grips with this- I'm just a bit confused about the 65 suspension chord. As far as I can tell, regarding the image at 11:22, the second bar has two chords in it. Dm7 in first inversion for the first two beats, and then GM root position for the rest of the bar. What exactly is being suspended here? All of the notes seem to be chord notes. I understand that the 5th and 6th are dissonant with each other, but it was my understanding that suspensions were non chord notes, prepared as chord notes in the previous chord, resolving by step into the next. The C (5) is prepared in the previous chord, and resolves by step in the next, but is surely a chord note of Dm7. The 6 (D) does not operate like a suspension in any way (as far as my understanding goes). Perhaps you are saying that harmony is not Dm7 at the start of the bar, and is perhaps V42?? Not sure about this- any help gratefully received! Ed
That's a fantastic question so please allow me to rant a little. It is simply a difference in perspective: instead of thinking of preexisting chord progressions elaborated with non-chord tones (as most modern textbooks frame things) the older view was that counterpoint is the cause and the chords are the effect. If we were to consider only the two upper voices, we would have a normal 7-6 suspension, as you pointed out. This type of suspension is very common at cadences. But how could we possibly add a third contrapuntal voice to this configuration? The new note must form a consonance with both of the upper voices because it occurs on the downbeat (the only way to include a dissonance on the downbeat would be to add another suspension). It turns out that ^4 is the only option for a bass tone beneath this particular 7-6 suspension: no other scale degree forms a consonance beneath both ^1 and ^2. But ^4 in the bass would dissonate against ^7 upon the resolution of the suspension, so the bass tone must change on the upbeat. And voila -- we have reconstructed the stock standard predominant-dominant-tonic progression using only linear counterpoint and consonant and dissonant intervals. "Tertian" harmony, stacks of thirds, and non-chord tones simply don't enter into the equation. This way of framing things also neatly explains why the II6/5 is such a common predominant chord --more common than the root position II7 or IV7.
@@JacobGran thanks jacob!! I think I've got you now! So the reason for this chord being a ''suspension'' chord, is down to the '7-6' suspension in the top voices?? Very interesting perspective and explanation. thanks! Ed
Master composers do not 'use' chords or non-harmonic tones for this purpose or that. The harmony is an inevitable outcome which is germane to the thematic material and form. We, after the fact, choose to distinguish between the various harmonies by way of analysis. The music itself does not need to be analyzed. We need to analyze music to better understand it.
I think that video lectures are very difficult pedagogically. You are presenting with only the information you have taken from theory books. You should be very explanatory for beginners. If you are preparing these lectures for those who know and advanced students, why should they follow these lectures if they know? You should be able to convey something to people rather than so much content. Thanks for our efforts anyway.!
The real magic starts when you create elaborated melodies over the suspensions.
Highly underrated channel, thank you sir.
Glad to hear you like it!
Amazing lessons as always!
Thank you for the kind words! Your continued viewership is much appreciated.
Really incredible channel, I love these!
13:23 Fux Gradus ad Parnassum pg 158 measure 3 and 8 seems to have a suspension of a kind you did not discuss (3-2 to 5-3?). Can you elaborate on why / how it works?
Good spot. I would probably figure these chords 9/3, depending on context. We could also call it a 3/2, but the figure "2" is often used when the bass tone is a dissonance (as with a 5/2 chord, for instance), which is not the case here. Bellermann ends up using this chord a couple of times in the exercise shown at the end of the video.
These chords are similar to a 9-8 melodic suspension, but Fux's second species bass line allows the bass to change at the moment of resolution. If the bass had not changed, the suspension would resolve to an incomplete triad on the upbeat, which is also ok in free composition, but for a strict exercise we would prefer a complete triad in every measure. This also conveniently gets around the issue of anticipating the tone of resolution, since the bass has moved on by the time the resolution takes place.
Merci.
Good evening Dr. Jacob. Is it possible to have you look at a four part example I worked to a figured bass on the figured bass worksheet?
What would be the correct doubling for a chord with a suspended 7th? For example, C major, the bass note is E and the figured bass is 7-6. Could the other voices, apart from the suspended one, be on Gs? This is a double 3rd for the 7th chord but when it resolves to 6 it is a doubled 5th for the tonic chord in first inversion which is more acceptable.
3:33 to make things clear, the dominant 7th is the only chord that can be freely struck; you don’t need to justify the dissonance? Any other 7th chord to replace both examples would be voice leading errors?
In a four voice texture, the figured bass symbol "7" in a context where it is clearly a 7-6 suspension implies an entire seventh chord, therefore there is also a chordal 5th (B in this case) that would move by step to double the 6th (C) in the chord of resolution or leap to another chord tone. If you wanted to avoid the fifth for whatever reason, then doubling the bass note (E) seems to be the most idiomatic.
I have another video on the topic of what Kirnberger called the "essential" dissonance of the dominant seventh chord (video 11 in this playlist). Thoroughbass authors give the privilege of freely struck (unprepared) dissonances to this class of seventh chord, which is almost entirely the dominant seventh quality, but sometimes also includes fully diminished seventh chords or the half-diminished leading tone seventh chord, for instance in the case of Albrechtsberger's exercises in "free composition" from video 13 in the playlist. Of course, we are drifting quite a bit now from the strict counterpoint of Fux.
Hi Jacob-
Just working through these again as it has been a while. In the 94-83 example. In bar 4 we have a dissonant 7thh above A. This 7th is not prepared, and yet is used as the preparation of another dissonance (4th). Why is this ok?
Similarly, in bar 3, we have a dissonance between G sharp and D (dim 5th) moving to another dissonant 4th between A and D. It is my understanding that suspensions should be consonant tones carried over to form dissonances, thhis doesnt seem to be the case here! please explain??
thanks again!
Great question, as usual. More liberties are given in thoroughbass (free composition) than in counterpoint (strict composition), and many of these videos of mine show them juxtaposed next to one another as if they are part of the same tradition, which is potentially a source of confusion. The D in m. 3 is easier to explain so I'll start there. There are two possible explanations: 1) D is the chordal seventh of an E dominant seventh chord, and it is therefore an "essential" ("Wesentliche") dissonance and has a privilege in 18th-c theory to be introduced freely and to act as a preparation of a suspension (see video 11 in the playlist); 2) The note D could also be seen to have been prepared as a consonant tenth in m. 2, and so acted as a dissonance in both mm. 3 and 4 before resolving down by step in m. 4.
Sechter's suspended G in m. 5 would not be appropriate in strict counterpoint. The preparation is a dissonant seventh, as you point out, and it also occurs on the last quarter note of the measure. However, Sechter allowed the chordal seventh (even of a minor quality seventh chord) to act as a preparation of a suspension in his thoroughbass examples when it followed a "circle of fifths" pattern like the sevenths that occurred on the weak beats in the example shown back around the 7:20 mark. The fact that it is prepared on the last quarter note probably has to do with the G-sharp of the previous measure; conceptually, the chordal seventh of an A minor chord could have been prepared as the third of an E chord moving through the circle of fifths like the pattern just mentioned, and could have been carried over mm. 3-5 just like the D in mm. 2-4, but we can't use both G-sharp and G-natural at the same time.
@@JacobGran Hi jacob,
Yes, I see the logic here. I understand that Sechter allowed the chordal 7th to act as a preparation for a suspension, but would this 7th usually have been prepared in the previous chord? (unlike the 7th G here). So can this unprepared 7th G be seen as an outlier, introduced like this to avoid a cross relation? Or, would this 7th G be seen as an essential dissonance , introduced freely and able to act as a preparation for a suspension, even though it is not the 7th of a dominant chord?
Hi Jacob. Firstly, thanks for another great vid. I was working on the first given exercise here but I'm stumped on the penultimate chord (7-, 4-3). Both the 7th and the 4th are dissonant above the bass, but I cant prepare them properly as neither feature in the previous chord (Em). What to do here?
thanks!
Good question. Let’s back up to the third to last measure; in the 9/7/4 chord there only the 9th and 7th resolve as the dash indicates that the fourth continues. That means we’re dealing with a cadential 6/4 triad for that measure (notes of a C major triad, not E minor), which is where the preparation for the fourth of the next measure comes from. The 7th in the penultimate measure is approached by step from the 8ve in the previous measure over a stationary bass, so it is actually a passing seventh (accented in this case) rather than a suspension and it too persists as the fourth resolves on the weak beat. I hope that helps.
@@JacobGran thanks very much for the explanation.
i have a question regarding the second exercise. measure 4, we have a 652 chord. Is the harmony for this bar G7 in third inversion? What are the suspended notes here? The C is a non-chord note , prepared in the previous chord but is consonant with the bass. The G is a chord note (I think), but is not consonant with the bass, and doesn't seem to resolve by step in the next chord. I have only really come across melodic suspensions thus far, so am still getting to grips with suspension chords!
thanks again!
Ed
@@edbowles5497 Yes, that is right. The chord for that measure is a 6/4/2 chord built on F (an inversion of a G dominant seventh), with the chordal third, B, suspended by the note C. You are right to point out that this C is more consonant with the bass note, F, than the tritone to which it resolves, but that is just a consequence of how rich tonal harmony can be. I mentioned something similar in the example starting at 2:35. In my opinion the C sounds more like a 2-3 suspension (or 7-6, depending on how it is realized) with respect to the chord tone D than a suspension relative to the bass.
As for the G not resolving, whenever the dissonance is shown as a "2" in the chord figures (like in 6/4/2 or 5/2, etc.) then the bass note is considered the dissonant note that must resolve, as the F does here (although not as a strict suspension, but as the "essential" dissonance of a dominant seventh chord; see the video on the counterpoint of dominant seventh chords for more on that). When the composer or analyst wants to indicate that the upper tone is the dissonance, it is typically figured as a "9" (as in 9/5/4 or something similar) instead of "2."
@@JacobGran Thanks yet again Jacob.
I understand what youre saying, although I'm a bit lost when you talk about hearing the C as a suspension relative to D rather than the bass. I thought that harmony was the primary factor in defining what is being suspended and what isn't, and that suspensions by their very nature must happen relative to the bass? If the C was a 7-6 or 2-1 (you said 2-3 in your answer, but i take it you mean 2-1??) relative to D, then wouldn't that imply that D was the third of the chord?
thanks for your help!
I could think of at least a few other chordal suspension combinations that aren't mentioned here, for example: 9/6 -> 8/5, 9/6/4 -> 8/5/3, 9/7/4 -> 8/6/3. Is this because they aren't very commonly used, or is there any other reason?
Btw, I find the idea of resolving suspensions above a moving bass line very interesting. Coming from a jazz background, I just view them as chord change up until now :)
The suspension chords I looked at it this video are definitely not an exhaustive list, but they are the main chord types that I found discussed in thoroughbass and counterpoint manuals. I suspect that 9/6 -> 8/5 is not mentioned because the top voices moving in parallel fourths and finishing on perfect consonances is not idiomatic of suspensions. Suspensions that resolve to imperfect consonances are preferred, like 9/4 -> 8/3. I think a 9/6/4 chord would have to be prepared as 8/5/3 in the previous chord and then resolve to 8/5/3, which would mean that we are suspending parallel chords a step apart, which will sound like parallel octaves and fifths. Maybe the bass could move beneath the resolution, but its hard to picture. 9/7/4 is definitely possible, especially if it is prepared as the upper chord members of a dominant seventh chord.
Actually it just occurred to me that the 9/6/4 could be prepared as 10/7/5 of a dominant seventh chord, which would sound great over a deceptive cadence.
@@JacobGran Would that be G 10/7/5 -> Am 9/6/4?
@@keyxmusic Yes that's what I was imagining.
👏
Hi Jacob. I am starting to get to grips with this- I'm just a bit confused about the 65 suspension chord. As far as I can tell, regarding the image at 11:22, the second bar has two chords in it. Dm7 in first inversion for the first two beats, and then GM root position for the rest of the bar. What exactly is being suspended here? All of the notes seem to be chord notes. I understand that the 5th and 6th are dissonant with each other, but it was my understanding that suspensions were non chord notes, prepared as chord notes in the previous chord, resolving by step into the next. The C (5) is prepared in the previous chord, and resolves by step in the next, but is surely a chord note of Dm7. The 6 (D) does not operate like a suspension in any way (as far as my understanding goes). Perhaps you are saying that harmony is not Dm7 at the start of the bar, and is perhaps V42?? Not sure about this- any help gratefully received!
Ed
That's a fantastic question so please allow me to rant a little. It is simply a difference in perspective: instead of thinking of preexisting chord progressions elaborated with non-chord tones (as most modern textbooks frame things) the older view was that counterpoint is the cause and the chords are the effect.
If we were to consider only the two upper voices, we would have a normal 7-6 suspension, as you pointed out. This type of suspension is very common at cadences. But how could we possibly add a third contrapuntal voice to this configuration? The new note must form a consonance with both of the upper voices because it occurs on the downbeat (the only way to include a dissonance on the downbeat would be to add another suspension). It turns out that ^4 is the only option for a bass tone beneath this particular 7-6 suspension: no other scale degree forms a consonance beneath both ^1 and ^2. But ^4 in the bass would dissonate against ^7 upon the resolution of the suspension, so the bass tone must change on the upbeat. And voila -- we have reconstructed the stock standard predominant-dominant-tonic progression using only linear counterpoint and consonant and dissonant intervals. "Tertian" harmony, stacks of thirds, and non-chord tones simply don't enter into the equation. This way of framing things also neatly explains why the II6/5 is such a common predominant chord --more common than the root position II7 or IV7.
@@JacobGran thanks jacob!! I think I've got you now! So the reason for this chord being a ''suspension'' chord, is down to the '7-6' suspension in the top voices??
Very interesting perspective and explanation. thanks!
Ed
🙂👍
"Classical" composers missed a huge opportunity to include 9th chords into classical music. A great loss.
mahler 9
Master composers do not 'use' chords or non-harmonic tones for this purpose or that. The harmony is an inevitable outcome which is germane to the thematic material and form. We, after the fact, choose to distinguish between the various harmonies by way of analysis. The music itself does not need to be analyzed. We need to analyze music to better understand it.
I think that video lectures are very difficult pedagogically. You are presenting with only the information you have taken from theory books. You should be very explanatory for beginners. If you are preparing these lectures for those who know and advanced students, why should they follow these lectures if they know? You should be able to convey something to people rather than so much content. Thanks for our efforts anyway.!